What is the limit as x approaches 1 of x^{(1/(1-x))} ?

The limit as x approaches 1 of x^{(1/(1-x))} is 1/e

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limit as x approaches 1 of x^{(1/(1-x))}

x \to 1 lim (x^{(\frac{1}{1 - x})})

\frac{1}{e}

Decimal Notation

0.36787 \dots

Solution steps

x \to 1 lim (x^{\frac{1}{1 - x}})

Apply exponent rules

= x \to 1 lim (e^{\frac{1}{1 - x} l n (x)})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

n = 1 \sum \infty n^{2} (\frac{2}{3})^{n}

\frac{d}{d x} (7 x - 1)

\frac{d}{d x} (x (x - a) ln (x + 1 + b^{2}))

\frac{d}{d x} (1 + x - y^{2})

\int \frac{x ^{n}}{n !} d x

What is the limit as x approaches 1 of x^{(1/(1-x))} ?
The limit as x approaches 1 of x^{(1/(1-x))} is 1/e